Novel logarithmic corrections to black hole entropy

Abstract

For a thermodynamic system, apart from thermal fluctuations, there are also fluctuations in thermodynamic volume when the system is in contact with a volume reservoir. For the case of black holes in anti-de Sitter spacetimes, the effect of thermal fluctuations on the entropy is well studied. The aim of this work is to compute novel logarithmic corrections to black hole entropy coming from simultaneous fluctuations of energy and thermodynamic volume. We work in the isothermal-isobaric ensemble and first obtain a general form of corrections to entropy which are valid for any thermodynamic system. Applying the formalism to Kerr black holes in AdS reveals that the black hole entropy gets corrected as: $\mathcal{S}=S_0-k\ln S_0+\cdots$ where $S_0$ is given by the Bekenstein-Hawking formula and $k=-1$. The same leading coefficient is also obtained in the canonical ensemble, i.e. by considering energy fluctuations alone. This coefficient is found to be unaltered in the slowly rotating and high temperature limits.

v1: 18 pages; v2 20 pages, typos corrected, references added, additional subsection added on Gauss-Bonnet black holes; v3: 25 pages, revised version, figures and references added

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Cited by in corpus (6)

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• Non-perturbative correction to the Horava-Lifshitz black hole thermodynamics
• Logarithmic corrections to the entropy function of black holes in the open ensemble
• Relativistic Correction to Black Hole Entropy
• Statistical ensembles and logarithmic corrections to black hole entropy
• Corrections to the Black hole entropy from a Bose Einstein condensate: a semi-classical phenomenological approach